Prime p₀= 281251674972221099 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 28 2 64 2 40 2 130 2 (?)
a_n: 0 2 12 14 42 44 108 110 150 152 282 284
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 284
Found by: desktop64
db: batch=69, k=12, 10 28 64 40 130

SPT(14)	281251628813547901	0 6 10 60 66 112 130 132 150 196 202 252 256 262	-46158673198
TPT(12)	281251630837170737	0 2 42 44 72 74 84 86 120 122 132 134	-44135050362
TPT(12)	281251636187113619	0 2 18 20 30 32 60 62 150 152 198 200	-38785107480
SPT(14)	281251643831996599	0 4 24 48 90 108 124 138 154 172 214 238 258 262	-31140224500
SPT(14)	281251646560283149	0 28 60 70 72 90 100 102 112 130 132 142 174 202	-28411937950
SPT(14)	281251652611963729	0 40 108 138 154 174 178 234 238 258 274 304 372 412	-22360257370
SPT(14)	281251692475386811	0 10 28 48 106 132 178 180 226 252 310 330 348 358	17503165712
SPT(14)	281251698968681803	0 10 70 88 94 120 124 150 154 180 186 204 264 274	23996460704
SPT(14)	281251703089858733	0 36 50 84 140 170 180 224 234 264 320 354 368 404	28117637634
SPT(14)	281251717220007761	0 30 62 90 108 146 156 272 282 320 338 366 398 428	42247786662
SPT(14)	281251736032700789	0 30 38 42 44 68 90 122 144 168 170 174 182 212	61060479690